Medical imaging of metabolic and biochemical activity within a patient is known as functional imaging. Functional imaging techniques include, for example, nuclear imaging such as Positron Emission Tomography (PET), Single Photon Computed Tomography (SPECT), functional magnetic resonance imaging (IMRI), and functional computed tomography (fCT). The reconstruction of a functional image from data acquired by functional imaging is often difficult because the data is often characterized by a small signal rates and small low signal-to-noise ratio. For nuclear imaging, for example, the count rate is limited by the amount of a radioactive substance that can be administered without harming the patient.
In addition, a functional image does not necessarily provide structural information. Thus, one evaluates a functional image often with the help of a structural image.
An overview of SPECT, PET systems, their combination with computer tomography (CT) systems as well as iterative image reconstruction for emission tomography is given in chapter 7, chapter 11, and chapter 21 of M. Weruick and J. Aarsvold, “Emission tomography: the fundamentals of PET and SPECT,” Elsevier Academic Press, 2004, the contents of which are herein incorporated by reference.
An overview of different reconstruction methods is given in R. C. Puetter et al., “Digital Image Reconstruction: Deblurring and Denoising,” Annu. Rev. Astro. Astrophys., 2005, 43: 139-194, the contents of which are herein incorporated by reference.